﻿Hello, I'm Mr. Langton and today, we're going to look at different ways of representing probabilities. All you're going to need is something to write with and something to write on. Try and make sure you're in a quiet space with no distractions. When you're ready, we'll begin. We'll start with the Try this activity. For each word, write down one sentence describing the chances of an event happening. Place your events in order from most likely to least likely. Pause the video and have a go. When you're ready, unpause it and we can go through it together. You can pause in three, two, one. Okay, how did you get on? I'll give you a few suggestions that I've got. You can see right now I'm holding a counter, it's red on one side and it's yellow on the other side. There is an even chance of my red and yellow counter landing on red. You could say it's equally likely it will land on yellow or red. Now a few other ones. It is unlikely that you can lick your own elbow. It is very unlikely that it'll be sunny in July. And my personal favourite, it is impossible to hum whilst holding your nose. I'm going to have to wait a second now while you try it, aren't you? So go on, hold your nose, see if you can hum. We can represent probabilities on a scale starting from impossible through to unlikely, to an even chance, through to likely, really likely, and a complete certainty. The probability scale looks like this. If something's impossible, we label it as zero. If something is absolutely certain, we call it one. We can label any probability we like somewhere along that scale. So an even chance would be halfway between zero and one. So it could be a half, or you could label it as 0.5, or you could label it as 50%. Probabilities can be labelled either as a fraction, a decimal, or as a percentage. So if we were to go here, halfway between impossible and an even chance, that's a quarter of the way along the scale, or 25%, or 0.25. If we were to describe that as a word, it's less than 50/50, it's more likely than impossible. It's probably something like unlikely. If you're looking at something up here maybe, maybe three quarters of the way, that's likely. It's more likely than not to happen. And again, it could be 75%, or 0.75, and you could label a probability at any part in between zero and one. We can't have anything over here, we can have anything back there. So zero is absolutely impossible and one is a certainty. Let's have a look now at these questions here. If I rolled a fair, six-sided dice, what's the probability that I'll roll an even number? So on a dice, I can roll one, two, three, four, five, or six. The even numbers are two, four, and six, so it's 50/50 chance, isn't it? Three of them are even, three of them are odd. There is an even chance that I roll an even number. I'm going to label that as a, because that's question a. Right, b. What is the probability that I roll a six? There's only one way to get a six. There are six possible options, only one of them is that six, so it's going to be somewhere down here. I've not measured it, so I can't be precise. I reckon about there is your one in six chance. In this case, it's much easier to represent that probability as a fraction, because if I have to write one sixth as a decimal, it gets messy, it's 0.16 recurring. It can be a little bit confusing working with decimals like that. Sometimes, it's much better to work with fractions. Let's label that one b. And finally, we'll move onto c. What is the probability that I roll a 10? Well, it's impossible to roll a 10, that is going to be zero. Let's put my c there on zero to say that it's not possible to do it. I can't have any probabilities outside that scale. Okay, now it's your turn. Pause the video and access the worksheet. Have a go at the questions and when you're done, we'll go through them together. Good luck. Okay, let's go over the answers. For each of the statements, you've got to state whether you agree or whether you disagree, and if you disagree, then you're going to rewrite them. The first one, if I hear thunder outside, it will certainly be raining. So that word certainly is what we're focusing on, and it's not quite true, is it? It will almost certainly be raining, it will probably be raining, but it's not certainly raining. Sometimes, you can hear thunder way away in the distance before it actually starts raining. So we can't use that word certainly, it will almost certainly be raining, or it will probably be raining, but we can't say that it will definitely be raining. The second one, if I roll a dice, I have an even chance of rolling a square number. If I roll the dice, I'm going to presume it's a six-sided dice, we've not been told otherwise, an even chance of rolling a square number, so just as much chance of getting a square number as not. So one and four are my square numbers. That's not an even chance, that's a less than even chance. So I could say I have a less than even chance of rolling a square number, it is unlikely I will roll a square number. You could say it is likely I will not roll a square number, so different ways that we can do that. Now the third one, I'm going to disagree again. It is impossible to toss a coin 10 times and get a head every time. It's very, very nearly impossible, it will take you an awful lot of tries to get there, but in the end, if you keep going and going and going and going, it is possible to do it, it's just very, very, very unlikely. So in each case, I disagree with the statement. Here we go, right, question two. Match the statements to the probability. Getting a head when a coin's tossed. So that's a 50/50 chance, or a half. Throwing a three on a six-sided dice. Now, this one can be a little bit tricky because some people want to say that there's a one in three chance, but it's not a one in three chance, there are six options when I roll the dice if I look back up here, let's use a different colour, there are six options, and one of them is a three, so actually, there is a one in six chance that I'll roll a three. Now, throwing an even number on a six-sided dice, there are three even numbers and three odd numbers, so that's going to be a 50/50 chance, isn't it? So there's an equal chance, so that probability is also going to be a half. Throwing a seven on a six-sided dice. That's not possible. Ain't possible, so that means it must be zero. And finally, tomorrow is Friday if today is Thursday. Well, that's a certainty. So that's a one. So you may have noticed there was a trick one in there, we did not end up using a third at all. Little bit sneaky for that one to be thrown in. We'll finish with the Explore activity. Which of the following probabilities are possible? How would you describe the probability in words? For those that are possible, think of an event that would have that probability. So pause the video and have a go. When you're ready, unpause it and we'll go through it together. You can pause in three, two, one. Okay, let's go through it. Let's start off with negative 0.5. That's impossible, we cannot have a probability like that, it does not represent a probability, so I'm going to cross that off now. Similarly, 2.5, 2.5 is greater than one and we can't have a probability if it's greater than one, so that's not a probability. 0.5, that is a probability. If I were to describe it in words, I'd say it was a 50/50 chance, or that it's equally likely. So think of something that's equally likely, so for example, tossing a coin and getting a head or a tail. Using my double sided counter that I showed you earlier, my red and yellow counter. They're things that would have a probability of 0.5. 150%, nope, we can't have 150%. That is way too big, because the largest percentage we could have would be this one here, 100%. So the probability that has got 100% chance of happening, if I roll a six-sided dice and I get a number smaller than seven. There's 100% chance that that will happen. Three quarters, yep. We can have that as a probability. If I was going to say that in words, I'd say that that's quite likely to happen. So something that is quite likely to happen is that it would be, do you know what? I'm going to go for spring instead of summer. I'm going to say that it's sunny in spring, because in summer, it's much more likely to be hotter, and in spring, I think three quarters of a chance it will certainly be sunny at some point in spring, won't it? 0.2, that is also perfectly fine to have as a probability. It's between zero and one, that's good. And it's less than a half, it's less than 0.5, so it's something that's quite unlikely to happen. So despite the fact that I'm ginger, it's unlikely that I'll get a sunburn in winter. It can happen, it did happen once before. But that's another story. Finally, one fifth is also fine to use as a probability. It's actually equivalent to 0.2, they are the same. So we could use the same example again, something that is unlikely to happen, not definitely not going to happen. Does not happen very often though.

When you roll a fair six-sided dice, it is harder to roll a six than a four.

In a group of ten people, the probability that at least two were born on the same day of the week is 1.

There is an even chance of it raining on any given day.

If I roll a fair six-sided dice, I am more likely to get an even number than an odd number.

Since a football team can either win, lose, or draw, the probability that they win must be one third.

Representing Probability

In this lesson, we will look at how we can represent probabilities as words and numbers.

Maths

Y9 Maths

Key Stage 3

Year 9

Representing probability

Probability

Statistics and probability

THEME

UNIT

Complementary events

Calculating probabilities

Theoretical probability and relative frequency

Theoretical probability and relative frequency (Part 2)

Comparing probabilities

Combined events and sample spaces (Part 1)

Combined events and sample spaces (Part 2)

Frequency trees

Calculating the probability of combined events

Combined Events and Tree Diagrams (Part 1)

Combined events and tree diagrams (Part 2)

Cala rolls a biased dice 40 times. It comes up with a three 14 times. Calculate the relative frequency of rolling a three.

Binh throws a biased dice 200 times. The theoretical probability of it landing on a 2 is 0.6. How many times would you expect her to throw a 2?

Yasmin has 200 daisy seeds to plant in her garden. The probability of a daisy growing is 0.8. How many daisies would you expect to grow?

There are 18 marbles in a bag. 13 of them are not green. What is the probability of selecting a green marble?

There are 100 cars in a car park. 40 of them are yellow. What is the probability of choosing a car that is not yellow?

What is the probability that this fair spinner lands on an odd number?

What is the probability that this fair spinner lands on a white triangle?

I roll a dice 50 times and it lands on a "six" 38 times. What is the relative frequency of getting a "six"?

I roll a fair six-sided dice. What is the probability I roll a 4 or a 6?

True or false: I am more likely to flip a coin and get "Heads" than I am to roll a six-sided dice and get a 4.

True or false: I am more likely to roll an even number than a prime number on an eight sided dice.

Lesson overview:Representing probability

Core Content

Probability: